When Woolworths collapsed just before Christmas 2008, the middle-class residents of Twickenham had big ideas for the town's abandoned shop. It would be an ideal new home, some thought, for the local farmers' market. If it couldn't be a permanent outlet for purveyors of organic rhubarb and locally churned butter, then what about a Marks & Spencer, one resident suggested to the local newspaper?

Therefore, plans to turn the old Woolies into a gleaming new Poundland store were greeted with dismay by local people. One told the Richmond & Twickenham Times: "We are never going to attract interesting or quality shops and businesses if the town is full of cheap bargain basement shops."

"Everyone was horrified," said one resident. "It really wasn't the sort of thing we wanted in Twickenham." A month later, Poundland opened for business and the only issue now, says the same resident, is the length of the queues at the tills. The Damascene conversion in Twickenham, south-west London, is being repeated across the country and, helped by the recession, it is fuelling dramatic growth for the West Midlands-based retailer. More than one in 10 Poundland shoppers is now drawn from the top AB social classes and at the height of the recession their numbers were up 22%. Poundland's stores are light, bright and sanitised, making it a respectable place for posher shoppers to be seen.

Last week the business, which has 260 stores – selling everything from Colgate toothpaste to books, garden gnomes and those glittery pink stetsons that are de rigueur on hen nights – was sold for £200m and the new owners have plans to turn it into a big national high street name, with 800 outlets – the same size Woolworths was when it went bust. Its recent track record, and the experience of Twickenham, suggests there's plenty of demand. Two years ago annual sales were £330m, but they are now more than £500m. Next year the chain expects to rake in £700m. Profits soared 27% to £20m in 2009 and are likely to be up another 40% this year.

Poundland eschews all the usual retail orthodoxy of offering a choice of "good, better and best" ranges to encourage shoppers to trade up. It does not aspire to be a specialist and there is no chance of a fancy loyalty card. It pulls in shoppers by stocking big brand bargains such as Tetley teabags and Heinz soup at – you guessed it – £1 (although chief executive Jim McCarthy dines out on the fact that the most frequently asked question in his stores is "How much does this cost?"). Those sales generate only wafer-thin profit margins, but the idea is that shoppers will be tempted to buy other, much more lucrative paraphernalia once they cross the threshold. And they do: 42% of sales are impulse purchases. The retailer has also benefited from others going bust: McCarthy reckons Poundland got a £60m boost from Woolworths' collapse.

Poundland may be the original and the biggest single price retailer – but it is not the only option for the new breed of savvy shopper. Aside from the many small, independent operators there is Pound World, with 80 shops and the cheaper 99p Stores chain.

The pound shop has its roots in American dollar stores, such as Dollar Tree and Dollar General, which started in the 1950s. Poundland, however, was founded by three former market traders from Wolverhampton: father and son Keith and Steve Smith and Dave Dodd, who set up a single shop in Burton upon Trent , Staffordshire, in 1990. Twelve years later, with 70 stores, the business was sold to a private equity group, Advent International, for £50m and the Smiths cashed out. Dodd sold his last shares last week for £24m.

Planet Retail analyst Bryan Roberts says the appeal of the store is that "it is a treasure hunt destination". Poundland's new respectability among the chattering classes is opening new doors. McCarthy said shopping centre landlords now want his stores. And better shops, in better places, will bring in posher shoppers. Even so, says, Roberts, Poundland is not, and never will be, entirely classless: "There are still some people," he says, "who would just not be seen dead in a Poundland."